Volume 63, Number 4, August 2003
|Page(s)||512 - 518|
|Published online||01 November 2003|
Short-period attractors and non-ergodic behavior in the deterministic fixed-energy sandpile model
Dipartimento di Energetica “S. Stecco” - Via S. Marta 3, I-50139 Firenze, Italy
2 INFM and Dipartimento di Fisica, Università di Roma “La Sapienza” P.le A. Moro 2, I-00185 Roma, Italy
3 INFM and International School for Advanced Studies (SISSA/ISAS) via Beirut 4, I-34014 Trieste, Italy
4 Laboratoire de Physique Théorique (UMR du CNRS 8627), Bâtiment 210 Université de Paris-Sud - 91405 Orsay Cedex, France
Accepted: 16 June 2003
We study the asymptotic behaviour of the Bak, Tang, Wiesenfeld sandpile automata as a closed system with fixed energy. We explore the full range of energies characterizing the active phase. The model exhibits strong non-ergodic features by settling into limit-cycles whose period depends on the energy and initial conditions. The asymptotic activity (topplings density) shows, as a function of energy density ζ, a devil's staircase behaviour defining a symmetric energy interval-set over which also the period lengths remain constant. The properties of the ζ- phase diagram can be traced back to the basic symmetries underlying the model's dynamics.
PACS: 05.70.Ln – Nonequilibrium and irreversible thermodynamics / 05.65.+b – Self-organized systems / 05.50.+q – Lattice theory and statistics (Ising, Potts, etc.)
© EDP Sciences, 2003
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